Calculating the inverse of a number has an important application in the division operation, particularly with a floating decimal. In particular, the result of the division of two numbers is obtained by simple multiplication of the dividend with the inverse of the divisor.
Typically, the division or calculation of the inverse I of a number D is attained by methods that can be classified into two main groups:
methods that work with subtraction and successive shifts, and
iterative methods, which are generally based on Newton's algorithm, by the recurrent equation: EQU In+1=In.times.(2-(D.times.In)),
in which In converges toward I.
In practice, with the subtraction and shifting methods, no more than 1 or 2 significant additional bits can be obtained at each step. Hence these methods require large-volume operator circuits, which are generally slow and are hard to integrate.
For scientific computers, in which the performance of the division operation is of prime importance, the iterative methods are generally preferred. If Newton's method is applied to standardized numbers, the precision of the result per iteration can be doubled. Nevertheless, each operation requires two multiplications performed in sequence, which hence cannot be parallelized. Moreover, to reduce the number of iterations, inverse tables are generally used to obtain the initial value of the iteration. In that case, the precision of the initial value is limited by the physical size of the inverse table, necessitating 2.sup.n-1 entries if the increment i of the table is selected to be equal to 2.sup.-n, for a precision on the order of 2.sup.2n, hence 2n significant bits.